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We report a refinement of Robertson-Schroedinger uncertainty relation via Wigner-Yanase skew information. Besides the well known quantum uncertainty arising from the noncommutativity of observables, there is classical uncertainty arising…
We present a diffeomorphism-invariant formulation of differential entropy for Riemannian spaces, providing a fine-grained, coordinate-independent notion of quantum information for continuous variables in physical space. To this end, we…
Complete measurement of a quantum observable (POVM) is a measurement of the maximally refined version of the POVM. Complete measurements give information on multiplicities of measurement outcomes and can be viewed as state preparation…
To maximize average information gain for a classical measurement, all outcomes of an observation must be equally likely. The condition of equally likely outcomes may be enforced in quantum theory by ensuring that one's state $\rho$ is…
The purpose of this paper is to study entanglement of quantum states by means of Schmidt decomposition. The notion of Schmidt information which characterizes the non-randomness of correlations between two observers that conduct measurements…
We discuss quantitatively the complementarity of information transmitted by a quantum system prepared in a basis state in one out of several different mutually unbiased bases (MUBs). We obtain upper bounds on the information available to a…
We postulate the existence of a universal uncertainty relation between the quantum and classical mutual informations between pairs of quantum systems. Specifically, we propose that the sum of the classical mutual information, determined by…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
We perform an information-theoretical analysis of quantum measurement processes and obtain the global information balance in quantum measurements, in the form of a closed chain equation for quantum mutual entropies. Our balance provides a…
We investigate different geometries and invariant measures on the space of mixed Gaussian quan- tum states. We show that when the global purity of the state is held fixed, these measures coincide and it is possible, within this constraint,…
Quantum information quantities, such as mutual information and entropies, are essential for characterizing quantum systems and protocols in quantum information science. In this contribution, we identify types of information measures based…
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a…
Complementarity restricts the accuracy with which incompatible quantum observables can be jointly measured. Despite popular conception, the Heisenberg uncertainty relation does not quantify this principle. We report the experimental…
Quantum mutual information (QMI) not only displays the mutual information in the system but also demonstrates some quantum correlation beyond entanglement. We explore here the two alternatives of multipartite quantum mutual information…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual…
We propose a new measure of quantum entanglement. Our measure is defined in terms of conditional information transmission for a Quantum Bayesian Net. We show that our measure is identically equal to the Entanglement of Formation in the case…
The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that…
We analyze tight informationally complete measurements for arbitrarily large multipartite systems and study their configurations of entanglement. We demonstrate that tight measurements cannot be exclusively composed neither of fully…